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 在這篇論文中我們主要探討Biharmonic Equation andPolyharmonic Equation 在有限區間解的行為就能Blow-up 。在第一章節中我們以介紹的方式瞭解現今數學家對此方程式中的探討跟瞭解並且給予正確的定義和主要定理的敘述，在第二章節裡我給予Lemmas 做先前的預備知識，在第三章節中我給予定理完整的證明，而在最後一個章節中列出相關文獻提供各位讀者參考。
 In he paper we are consider for Biharmonic Equations and Polyharmonic Equation in the finite interval will Blow-up.In the chapter 1 we are introduce the main theorem and to definition equation.In the chapter we give some Lemmas in order to proofs theorems 1.1 and 1.2In the chapter 3 we proofs of theorem 1.1 and 1.2,and the last chapter we give the references
 CONTENTS1. INTRODUCTION……………………………………………2~52. PRELIMINARIES……………………………………………5~133. MAIN THEOREM……………………………………………13~18REFERENCE……………………………………………………………18~19
 ReferencesSattinger, D.H.:Conformal metric in R2 with prescribed carvature. Indi-ana Univ. Math. J. 22, 1-4 (1972).Oleinik, O.A.:On the equantion 4u+K(x)eu = 0. Russian Math. Surveys33, 243-244 (1978).W-M.Ni, On the elliptic equation 4u + K(x)e2u = 0 and conformal met-rics with prescried Gaussian, Invent, Math. 66 (1982), 343-352.T.Kusano and S. Oharu, Bounded entire solutions of second order semi-linear elliptic equation with application to a parabolic intial value problem,Indiana Univ. Math. J. 34 (1985) 85-95.W-M.Ni, On the elliptic equation 4u+K(x)un¡2n+2 = 0, its generalizations,and applications in geometry, Indiana Univ. Math. J. 31 (1982), 493-529.R.McOwen,On the equation 4u + K(x)e2u = f and prescribed negativecarvature in R2, J. Math. Anal.Appl. 103 (1984), 365-370.Kazdan, J., Prescribing the curvature of a Riemannian manifold, NSF-CBMS Regional Conference Lecture Notes 57 (1985).Cheng, K.-S. and Lin, J.-T., on the elliptic Equation 4u = K(x)u¾ AND4u = K(x)e2u;Trans. of the Amer. Math.Cheng,K.-S. and Smoller, Joel A.,Conformal metrics with prescribed Gaus-sian curvature on R2,Trans.Math.Soc. 336 (1993), no.1,219-251.Lin, C.-S., A classi‾cation of solution of a conformally invariant fourthorder equation in Rn, Comment. Helv. 73(1998) 206-231 電子全文 國圖紙本論文 推文當script無法執行時可按︰推文 網路書籤當script無法執行時可按︰網路書籤 推薦當script無法執行時可按︰推薦 評分當script無法執行時可按︰評分 引用網址當script無法執行時可按︰引用網址 轉寄當script無法執行時可按︰轉寄    top
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